Unable to reinstall OS X Yosemite

In case your Recovery partition isn't working properly, and assuming your firmmware supports Internet Recovery, try forcing your Mac to boot into Internet Recovery. See if that works any better.

Before you sell or give away your computer, in addition to the steps listed in this support article, take these steps:

1. Run Apple Diagnostics or the Apple Hardware Test. The buyer will do this (or he should), and you don't want to be surprised by the results.

2. Reset the PRAM and the SMC, which might contain personal information.

3. If you set a firmware password, remove it by running Firmware Password Utility in Recovery mode.

4. If you activated FileVault in OS X 10.7 or later, turn it off.

5. If you use Boot Camp, the partition must be deleted.

6. If you created any other data partitions on the internal drive, remove them in Disk Utility.

7. If the machine has an internal hard drive, erase the one remaining data partition with the option to zero out data. An SSD doesn't need to be zeroed.

8. Remove the machine from your list of registered products. If it's still covered by an AppleCare Protection Plan, transfer the coverage to the new owner by following the instructions in the AppleCare Terms and Conditions (under the heading "Transfer of Plan.")

Also note:

You can't legally or practically transfer any software downloaded from the Mac App Store to the new owner of the machine, even if it was free. That includes OS X, so if you upgraded to OS X 10.7 or later, you must reinstall an older OS, either from the installation media, if applicable, or by starting up in Internet Recovery mode (option-command-R at the startup chime.) If you installed from physical media, deliver those to the new owner.

Replacements for the original media can be ordered from Apple.

If the machine shipped with OS X 10.4 or 10.5, then you may be able to install on it from a retail Snow Leopard disc (which you must then transfer to the buyer.) To run Snow Leopard, the machine needs at least 1 GB of memory. The buyer should understand that if he doesn't get the original media from you, he won't get the bundled iLife applications or the Apple Hardware Test.

The new owner will have to redownload any software that came from the App Store, if applicable, including OS X upgrades, under his or her Apple ID. If you ever updated the bundled iLife applications (Garage Band, iMovie, and iPhoto) through the App Store, you can't transfer those either. The buyer will have to purchase them.